Robust Tensor Recovery via A Nonconvex Approach with Ket Augmentation and Auto-Weighted Strategy

In this talk, we introduce a nonconvex tensor recovery approach, which employs the powerful ket augmentation technique to expand a low order tensor into a high-order one so that we can exploit the advantage of tensor train (TT) decomposition tailored for high-order tensors. Moreover, we define a new nonconvex surrogate function to approximate the tensor rank, and develop an auto-weighted mechanism to adjust the weights of the resulting high-order tensor’s TT ranks. To make our approach robust, we add two modeunfolding regularization terms to enhance the model for the purpose of exploring spatio-temporal continuity and self-similarity of the underlying tensors. Also, we propose an implementable algorithm to solve the proposed optimization model in the sense that each subproblem enjoys a closed-form solution. A series of numerical results demonstrate that our approach works well on recovering color images and videos.

报告人简介：凌晨 : 杭州电子科技大学理学院（二级）教授，博士生导师。曾任：杭州电子科技大学理学院院长、中国运筹学会数学规划分会副理事长、中国经济数学与管理数学研究会副理事长、中国运筹学会理事、中国系统工程学会理事、浙江省数学会常务理事、浙江省教育厅数学教育指导委员会委员（第一、二届）等。现任国际期刊 Pacific Journal of Optimization编委、Statistics, Optimization & Information Computing编委。近十余年来，连续主持国家自科基金和浙江省自科基金各4项(其中含省基金重点项目1项)。成果发表在SCIENCE CHINA-Mathematics、Math. Program.、SIAM J. Optim.、SIAM J.Matrix Anal.and Appl.、J.Sci.Comput.、Comput.Optim.Appl.、J.Optim.Theory Appl.、J.Global Optim.、Appl.Math.Comput.等国内外重要刊物